Ok, let me help. The Amiga has the ability to have bigger screens than the monitor can show at once. It can also move those 'screens' in any direction, and therefore show different bits of themselves on the monitor. Think of it like moving a slide around on a microscope, you can't see the whole slide at once through the eyepiece, so you move it around.

The Amiga can also overlay these screens on top of one-another, letting bits of the lower screens show through the transparent bits of the upper screens. For a real-world example, think of two clear plastic overhead projector sheets, one on top of the other. The top one is just the ball, and the bottom sheet is the grid. By moving the top sheet around, you create the effect that the ball is bouncing around the grid.

To emulate the ball rotating, the Amiga used one of it's other graphical tricks: palette cycling. The ball is actually made up of many thin strips of colour. Think of these strips as Colour1 to Colour30, all of the colours are painted white, except for a few evenly spaced red ones. To make the ball 'rotate' the colours assigned to Colour1 thru Colour30 are shifted one place to left (or right) a few times a second. This created the illusion that the ball is rotating, when in fact it's not.

All of this is done via hardware routines in the custom graphics chip, and uses almost no CPU time at all. It may not have been done how people think it was done, but it was still an impressive demo of the hardware regardless.

Basically, it's all smoke and mirrors, and please ignore the man behind the curtain.